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Hot electrons dominate the ultrafast ($\sim$fs-ps) optical and electronic properties of metals and semiconductors and they are exploited in a variety of applications including photovoltaics and photodetection. We perform power-dependent third harmonic generation measurements on gated single-layer graphene and detect a significant deviation from the cubic power-law expected for a third harmonic generation process. We assign this to the presence of hot electrons. Our results indicate that the performance of nonlinear photonics devices based on graphene, such as optical modulators and frequency converters, can be affected by changes in the electronic temperature, which might occur due to increase of absorbed optical power or Joule heating.